how to determine if a function is positive (for the integral test)

to use the integral test to prove the convergence or divergence of a given series, three conditions must be met, the first is it must be continuous, second, it must be positive, and third it must be decreasing...

I know how to determine number one and number three, but i havent been sure about how to determine or prove that the series is positive (or the function being used to integrate anyways), this should be simple and right under my nose since i cannot find the answer in any of my books, any insight? thanks

Re: how to determine if a function is positive (for the integral test)

Originally Posted by bishopdan26

I know how to determine number one and number three, but i havent been sure about how to determine or prove that the series is positive

Well, any mathematical theory containing basic arithmetic is undecidable, so there is no general algorithm to find out if a function is nonnegative and to prove this fact if it is. Therefore, you can only prove it in certain cases. You said that you can prove that a series is decreasing, so you can prove inequalities. The claim that a function is nonnegative is also an inequality...